15.1.19 problem 19

Internal problem ID [2859]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 5, page 21
Problem number : 19
Date solved : Monday, January 27, 2025 at 06:20:22 AM
CAS classification : [_separable]

\begin{align*} \tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 40

dsolve(tan(x)*sin(x)^2+cos(x)^2*cot(y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \arcsin \left (\frac {\sqrt {2}\, \sqrt {\frac {1}{1+\cos \left (2 x \right )}}\, {\mathrm e}^{\frac {-1+\cos \left (2 x \right )}{2+2 \cos \left (2 x \right )}}}{c_1}\right ) \]

✓ Solution by Mathematica

Time used: 12.583 (sec). Leaf size: 24

DSolve[Tan[x]*Sin[x]^2+Cos[x]^2*Cot[y[x]]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (\frac {1}{8} c_1 e^{-\frac {1}{2} \sec ^2(x)} \sec (x)\right ) \]